Volume of a Cylinder Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Volume of a Cylinder.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The amount of three-dimensional space inside a cylinder, found by multiplying the area of the circular base by the height.

Imagine stacking hundreds of identical circular coins into a tall tower. Each coin is a thin circle with area \pi r^2, and stacking h units high gives you a cylinder. The volume is just the area of one coin times the height of the stack.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Volume of a cylinder = base area \times height. This principle works for any prism-like shape.

Common stuck point: Make sure h is the perpendicular height (straight up), not the slant height.

Worked Examples

Example 1

easy
A cylinder has a radius of 4 cm and a height of 10 cm. Find its volume. Use \pi \approx 3.14.

Solution

  1. 1
    Step 1: Write the formula for the volume of a cylinder: V = \pi r^2 h.
  2. 2
    Step 2: Substitute the values: V = \pi \times 4^2 \times 10 = \pi \times 16 \times 10 = 160\pi.
  3. 3
    Step 3: Approximate: V \approx 160 \times 3.14 = 502.4 cm³.

Answer

V = 160\pi \approx 502.4 cm³.
The volume of a cylinder is the area of the circular base (\pi r^2) multiplied by the height (h). This formula makes intuitive sense: you are stacking up infinitely many thin circular disks of area \pi r^2 to a total height h.

Example 2

medium
A cylindrical water tank holds 2000\pi liters. Its height is 20 m. Find the radius of the tank.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A soup can has a diameter of 8 cm and a height of 12 cm. Find the volume. Leave your answer in terms of \pi.

Example 2

hard
Two cylinders have the same volume. Cylinder A has radius 3 and height 16. Cylinder B has height 4. Find the radius of Cylinder B.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

area of circlevolume